PHY1025 Mathematics Skills
2011-2012
Code: PHY1025
Level: 1
Title: Mathematics Skills
Instructors:
Dr P.G. Petrov
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration:
T1:01-11
Availability: unrestricted
Background Assumed: -
Total Student Study Time
150 hours, to include:
22×1-hour lectures;
45 hours directed self-study;
11 hours of problems class support;
3 hours of tutorial support;
69 hours private study.
Aims
All physicists must possess a sound grasp of mathematical methods and a good level of
'fluency' in their application. This module covers areas such as
differential calculus, complex numbers, and matrices that have wide applicability throughout
physics. It provides a firm foundation on which the follow-up module PHY1026 will build,
and emphasises problem solving with examples taken from physical sciences.
Intended Learning Outcomes
Students will be able to:
- Module Specific Skills:
- make efficient use of the techniques and concepts of foundation-level
mathematics: algebra, trigonometry and calculus;
- make series expansions of simple functions and determine
their asymptotic behaviour;
- perform basic arithmetic and algebra with complex numbers;
- perform basic operations on matrices and solve systems of
simultaneous linear equations;
- evaluate single, double and triple integrals in straightforward cases;
- evaluate partial derivatives.
- Discipline Specific Skills:
- tackle, with facility, mathematically formed problems and their solution.
- Personal Transferable Skills:
- manage their time effectively in order to meet fortnightly deadlines
for the completion of homework and develop appropriate coping strategies;
- work co-operatively and use one another as a learning resource.
Learning / Teaching Methods
Lectures,
e-Learning resources (ELE PHY1025),
and problems classes.
Assessment and Assignments
Contribution | Assessment/Assignment | Size (duration/length) | When |
20% | Problem Sets | 5×6-hour sets | Fortnightly |
15% | Mid-term Test 1 | 30 minutes | Week T1:04 |
15% | Mid-term Test 2 | 30 minutes | Week T1:08 |
50% | Final examination | 120 minutes | Week T2:00 |
Formative | Guided self-study | 5×3-hour packages | Fortnightly |
Syllabus Plan and Content
- Foundation Mathematics (Self-Study Pack)
- Algebra
- Trigonometric functions
- Trigonometry and the binomial theorem
- Matrices
- Matrix addition, subtraction, multiplication
- Inversion of matrices
- Applications to the solution of systems of homogeneous and inhomogeneous linear equations
- Evaluating numerical determinants
- Introduction to eigenvalues and eigenvectors
- Calculus with a Single Variable
- Differentiation
- Integration I
- Integration II
- Calculus with Several Variables
- Partial differentiation
- Coordinate systems in 2- and 3-dimensional geometries -
Cartesian, plane-polar, cylindrical and spherical polar
coordinate systems
- Two-dimensional and three-dimensional integrals and their application
to finding volumes and masses
- Series Expansions, Limits and Convergence
- Taylor and Maclaurin series, expansions of standard functions
- Curve Sketching
Core Text
Stroud K.A. (
2007),
Engineering Mathematics (
6th edition),
Paulgrave,
ISBN 1-4039-4246-3 (UL:
510.2462 STR)
Supplementary Text(s)
Arfken G.B. and Weber H.J. (
2001),
Mathematical methods for physicists (
5th edition),
Academic Press,
ISBN 0-120-59826-4 (UL:
510 ARF)
Spiegel M.R. (
1971),
Advanced Mathematics for Engineers and Scientists,
Schaum Outline Series, McGraw-Hill,
ISBN 0-070-60216-6 (UL:
510 SPI)
Stroud K.A. and Booth D.J. (
2003),
Advanced Engineering Mathematics (
4th edition),
Paulgrave,
ISBN 1-4039-0312-3 (UL:
510.2462 STR)
IOP Accreditation Compliance Checklist
- MT-01: Trigonometric functions.
- MT-02: Hyperbolic functions.
- MT-04: Series expansions, limits and convergence.
- MT-11: Matrices to the level of eigenvalues and eigenvectors.
Formative Mechanisms
Students monitor their own progress by attempting the problem sets
which will be discussed in classes. Students who need additional
guidance are encouraged to discuss the matter with the lecturer or their tutor.
Evaluation Mechanisms
The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.